A021174 Expansion of 1/((1-x)(1-2x)(1-6x)(1-7x)).

1, 16, 173, 1592, 13461, 108192, 841261, 6392584, 47771141, 352537328, 2576599389, 18689228376, 134742802741, 966708860224, 6908017500557, 49202455443368, 349495185871461, 2476934287969680, 17521347937528765

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (16,-83,152,-84).

Formula

a(0)=1, a(1)=16, a(2)=173, a(3)=1592; for n>3, a(n) = 16*a(n-1) -83*a(n-2) +152*a(n-3) -84*a(n-4). - Vincenzo Librandi, Jul 07 2013

a(0)=1, a(1)=16; for n>1, a(n) = 13*a(n-1) -42*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013

a(n) = (2*7^(n+3) - 3*6^(n+3) + 3*2^(n+3) - 2)/60. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 -  7 x)), {x, 0, 20}], x]  (* Vincenzo Librandi, Jul 07 2013 *)
LinearRecurrence[{16, -83, 152, -84}, {1, 16, 173, 1592}, 20] (* Harvey P. Dale, May 29 2019 *)

Prog

(Magma) I:=[1, 16, 173, 1592]; [n le 4 select I[n] else 16*Self(n-1)-83*Self(n-2)+152*Self(n-3)-84*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-6*x)*(1-7*x)))); // Vincenzo Librandi, Jul 07 2013

Crossrefs

Sequence in context: A238725 A221789 A018209 * A021374 A253343 A215687

Adjacent sequences: A021171 A021172 A021173 * A021175 A021176 A021177

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved